Fabian

 41 What is the 'implicit function theorem'? 33 How to calculate the derivative of this integral? 27 What is the purpose of Stirling's approximation to a factorial? 20 Prove that $\sum_{k=1}^{\infty} \large\frac{k}{\text{e}^{2\pi k}-1}=\frac{1}{24}-\frac{1}{8\pi}$ 20 How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$?

### Reputation (21,499)

 +10 The series $\sum_{n=2}^{\infty }\frac{1}{\log (n!)}$ +10 How to calculate the derivative of this integral? +10 Relation between Hankel transform and Fourier transform +10 Determinant of matrix $(x_j^{n-i}- x_j^{2n-i})_{i,j=1}^{n}$

### Questions (16)

 31 Simpler way to evaluate the Fourier transform of $\exp\left(i e^x\right)$? 22 Asymptotic expression of an oscillatory integral 14 Chebyshev's versus Markov's inequality 7 Connection between Legendre polynomial and Bessel function 7 What is u-substitution?

### Tags (263)

 378 integration × 108 141 complex-analysis × 51 347 calculus × 101 110 linear-algebra × 49 177 real-analysis × 35 102 multivariable-calculus × 25 159 asymptotics × 38 97 ordinary-differential-equations × 43 144 definite-integrals × 41 87 sequences-and-series × 17

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